The best thing to do is to ask the child to help clean up the walls. Asking for his admission isn't productive since his goal is only to escape from punishment.
Your question touches on fundamental concepts of child-raising that will affect your child for a lifetime, and I commend you for taking this seriously enough to write. You must not punish him unless you are 100% certain he did it.
Also, he did not get punished for what he did, because he told the truth and said he was sorry.
Don't worry – even though you may lose this "battle," you are more likely to win the war.
We suspected our 4-year-old, and asked him if he did it. We are not positive he did it, but he has a guilty look and it is very unlikely that another child did it. Not to necessarily get him to tell the truth regarding one incident of coloring on the wall.
Use the straw man technique to develop a main character who gets into a similar situation as your son – e.g.
“Once upon a time there was a boy called Mikey...” The "plot" of each story is, naturally, that the boy lied because he was afraid – and then he told the truth and everyone was so proud of him!
If he tells the truth, then make a big deal about it – e.g.